Punjab Technical University 2006-1st Sem M.C.A -COMPUTER MATHEMATICAL FOUNDATION - Question Paper

COMPUTER MATHEMATICAL FOUNDATION
MCA-104, first Semester(2096)

Time: 3 Hours Max Marks:75

Note: The ques. paper will consist of 2 parts A and B.
(a) Part A is compulsory and have 15 short ans questions(40-60 words) of two marks every.
(b) Part-B have 12 long ans ques. of five marks each, out of which candidate have to attempt nine ques..

Part – A (15x2=30)
1.
(i) If A={f{f}},then obtain P(A).
(ii) Draw Venn diagram for B-A and AUB.
(iii) Define relation with the help of an example.
(iv) Define inverse relation with the help of an example.
(v) Give 1 example of a Proposition and non-proposition every.
(vi) If P(x) is the statement “(n+1)(n+2) is even”, then what is P(3)?
(vii) Draw a truth table for XOR.
(viii) Differentiate ranging from tautology and contradiction.
(ix) What is the use of existential quantifier?
(x) Differentiate simple and multigraph.
(xi) What is chromatic number?
(xii) What is graph coloring?
(xiii) Define diagonal matrix with the help of an example.
(xiv) Define skew symmetric matrix with the help of an example.
(xv) Give example of matrices A and B such that AB=BA.

Part-B (Marks: five each)
2. Prove that (AUB)c=AcnBc.
3. Let A and B be any 2 disjoint sets then prove that
|AUB|=|A|U|B|-|AnB|
4. If R is the relation in NxN described by (a,b)R(c,d) if a+d=b+c,show that R is an equivalence relation.
5. Give example of a Relation, which is both equivalence, and partial order relations.
6. Prove by induction that
2+5+8+11……+(3n-1)=n(3n+1)/2 for all natural number.
7. Prove that the sum of the cubes of 3 consecutive integers is divisible by 9.
8. Prove by truth table that p?(q^r)=(p?q)^(p?r).
9. Prove that for any 2 matrices A and B,
(A+B)c=Ac+Bc.
10. Solve the subsequent systems of equations, with Gauss elimination Method: x+y+z=1,x+2y+3z=6 and x=3y=4z=6
11. Define Bipartite graph. When it is stated to be Complete Bipartite graph? Also draw K3,4 Complete Bipartite graph.
12. Discuss Matrix representation of Multigraph with a suitable example.
13. Let f(x)=x2-5x+6. obtain (A) if

A= one two 2
2 one 2
2 two 1

Earning:   Approval pending.